Use Fraction Addition/subtraction Rules To Complete The Following. Show Work.a. 5 9 − 1 4 \frac{5}{9} - \frac{1}{4} 9 5 ​ − 4 1 ​ B. 1 2 + 4 9 \frac{1}{2} + \frac{4}{9} 2 1 ​ + 9 4 ​ C. 1 9 + 19 81 \frac{1}{9} + \frac{19}{81} 9 1 ​ + 81 19 ​ D. 2 15 − 4 45 \frac{2}{15} - \frac{4}{45} 15 2 ​ − 45 4 ​

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Introduction

Fractions are an essential part of mathematics, and understanding how to add and subtract them is crucial for solving various mathematical problems. In this article, we will delve into the world of fraction operations, focusing on the rules for adding and subtracting fractions. We will explore four different scenarios, each requiring the application of these rules to find the final result.

Fraction Addition/Subtraction Rules

Before we dive into the examples, let's review the basic rules for adding and subtracting fractions:

  • To add or subtract fractions, they must have a common denominator.
  • If the fractions have different denominators, we need to find the least common multiple (LCM) of the two denominators.
  • Once we have the LCM, we can rewrite each fraction with the LCM as the denominator.
  • Now that the fractions have the same denominator, we can add or subtract the numerators.
  • The resulting fraction will have the LCM as the denominator.

Example a: 59−14\frac{5}{9} - \frac{1}{4}

Introduction

Fractions are an essential part of mathematics, and understanding how to add and subtract them is crucial for solving various mathematical problems. In this article, we will delve into the world of fraction operations, focusing on the rules for adding and subtracting fractions. We will explore four different scenarios, each requiring the application of these rules to find the final result.

Fraction Addition/Subtraction Rules

Before we dive into the examples, let's review the basic rules for adding and subtracting fractions:

  • To add or subtract fractions, they must have a common denominator.
  • If the fractions have different denominators, we need to find the least common multiple (LCM) of the two denominators.
  • Once we have the LCM, we can rewrite each fraction with the LCM as the denominator.
  • Now that the fractions have the same denominator, we can add or subtract the numerators.
  • The resulting fraction will have the LCM as the denominator.

Example a: 59−14\frac{5}{9} - \frac{1}{4}

To solve this problem, we need to find the LCM of 9 and 4. The LCM of 9 and 4 is 36. We can rewrite each fraction with 36 as the denominator:

59=5×49×4=2036\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}

14=1×94×9=936\frac{1}{4} = \frac{1 \times 9}{4 \times 9} = \frac{9}{36}

Now that the fractions have the same denominator, we can subtract the numerators:

2036−936=20−936=1136\frac{20}{36} - \frac{9}{36} = \frac{20 - 9}{36} = \frac{11}{36}

Example b: 12+49\frac{1}{2} + \frac{4}{9}

To solve this problem, we need to find the LCM of 2 and 9. The LCM of 2 and 9 is 18. We can rewrite each fraction with 18 as the denominator:

12=1×92×9=918\frac{1}{2} = \frac{1 \times 9}{2 \times 9} = \frac{9}{18}

49=4×29×2=818\frac{4}{9} = \frac{4 \times 2}{9 \times 2} = \frac{8}{18}

Now that the fractions have the same denominator, we can add the numerators:

918+818=9+818=1718\frac{9}{18} + \frac{8}{18} = \frac{9 + 8}{18} = \frac{17}{18}

Example c: 19+1981\frac{1}{9} + \frac{19}{81}

To solve this problem, we need to find the LCM of 9 and 81. The LCM of 9 and 81 is 81. We can rewrite each fraction with 81 as the denominator:

19=1×99×9=981\frac{1}{9} = \frac{1 \times 9}{9 \times 9} = \frac{9}{81}

1981=19×181×1=1981\frac{19}{81} = \frac{19 \times 1}{81 \times 1} = \frac{19}{81}

Now that the fractions have the same denominator, we can add the numerators:

981+1981=9+1981=2881\frac{9}{81} + \frac{19}{81} = \frac{9 + 19}{81} = \frac{28}{81}

Example d: 215−445\frac{2}{15} - \frac{4}{45}

To solve this problem, we need to find the LCM of 15 and 45. The LCM of 15 and 45 is 45. We can rewrite each fraction with 45 as the denominator:

215=2×315×3=645\frac{2}{15} = \frac{2 \times 3}{15 \times 3} = \frac{6}{45}

445=4×145×1=445\frac{4}{45} = \frac{4 \times 1}{45 \times 1} = \frac{4}{45}

Now that the fractions have the same denominator, we can subtract the numerators:

645−445=6−445=245\frac{6}{45} - \frac{4}{45} = \frac{6 - 4}{45} = \frac{2}{45}

Q&A

Q: What is the least common multiple (LCM) of two numbers? A: The LCM of two numbers is the smallest number that is a multiple of both numbers.

Q: How do I find the LCM of two numbers? A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

Q: What is the difference between adding and subtracting fractions? A: The difference between adding and subtracting fractions is that when adding fractions, you add the numerators, and when subtracting fractions, you subtract the numerators.

Q: How do I add and subtract fractions with different denominators? A: To add and subtract fractions with different denominators, you need to find the least common multiple (LCM) of the two denominators and rewrite each fraction with the LCM as the denominator.

Q: What is the resulting fraction when adding or subtracting fractions? A: The resulting fraction when adding or subtracting fractions is the fraction with the least common multiple (LCM) as the denominator.

Conclusion

In this article, we have explored the world of fraction operations, focusing on the rules for adding and subtracting fractions. We have reviewed the basic rules for adding and subtracting fractions and have applied these rules to four different scenarios. We have also answered some common questions about fraction operations. By mastering fraction operations, you will be able to solve various mathematical problems with ease.